Animate mesh so it's parts appear from left to right
There are at least 2 ways to do it: With a Boolean modifier or with a Build modifier.

You could use a Boolean modifier (Difference mode). It looks like you'll avoid bugs if your boolean object (my cube) is a bit subdivided:



To make the cube transparent in Solid mode, choose Viewport Display > Wire, to make it invisible in Render, disable all its Ray Visibility options.



For a different kind of effect you could use the Build modifier, it will make your object gradually appear, face by face, as if you were building it:


Model your object, in Edit mode put the 3D cursor on its tail:





Select all, in the Mesh menu > Sort Elements > Cursor Distance. It will sort the vertices from the tail to the head.





Give your object a Build modifier, play with the parameters so that the object appears gradually. You can animate with some keyframes on these values.